 Let me start talking about the contaminant transport in porous media. I am sure that most of you will agree with me that flow of water through porous media has already been studied very extensively and where do you use these concepts? You use these concepts in seepage analysis, consolidation theory and stability of different geotechnical engineering problems where the migration of the flow of water is taking place which creates a media as saturated or unsaturated. So this is very well understood mechanism of the phenomena. So in short, the concept of hydraulic conductivity are very well established. You know the laws which can be used for describing the hydraulic conductivity or coefficient of permeability of the porous system. By the same time, we have been talking about that why because of environmental degradation, the chemical flux or the chemical flow in the soils or the porous system is becoming quite important. Most of the activities related to present in the sterilization and socialization is causing lot of contaminants or the chemicals to flow in the porous system or the porous media. So that is why I say that chemical flows in soils or the porous system are also gaining lot of importance. So this is where actually we have to do something to incorporate the effect of flow of chemicals in the porous system which we will be talking in the review of contaminant transport in porous media. Now why it is so and some of the important examples of this type of situation are most of the industrial activities like waste storage, remediation of contaminated sites and leaching phenomena and so on. So these are becoming quite important activities and that is the reason that one should study how contaminant migrate in the porous system. Now it is important to understand that what causes this flow to take place or to occur. So basically contaminants are dissolved either in organic or organic substances in the solvent and the solvents are either water or the fluids. So various concentration units are used to define the relative amounts of contaminants which are present in the solvent. The first way of defining the concentration is mass concentration where you use the term milligrams of contaminant in 1 liter of water this is known as milligrams per liter. Now another way of defining this is parts per million PPM or if you change the word parts per trillion this becomes PPT or parts per billion PPB and so on. So essentially parts per million PPM is nothing but grams of solution divided by million grams of the solution where the contaminants are in this form grams of solution. Now what are the types of flow through porous media which can take place. Now this is assumption which most of the time we make that if flow does not change the fabric and stress state of the porous media then the flow rate J relates linearly to its corresponding driving force X. Now this is the most generalized form of the flow which takes place through a new system where J is nothing but the flow rate and phi I have defined as the flux and X happens to be the driving force. So phi is the conductivity coefficient for flow. Now this coefficient will depend upon the type of energy which is flowing through the porous media. So for that matter you are very well conversant and convenient with the flow of fluid there is a control volume and this is a soil sample or rock sample one side of this head H1 is connected the other side of this head H2 is connected. The differential head between H1 and H2 gives you delta H and if length of the sample is known you can find out the value of Q. Now Q is nothing but the flow of C page alright. So we say that Q equal to some constant multiplied by delta H upon L where delta H upon L is nothing but the hydraulic gradient and then we say that Darcy's law is valid for this type of situation. Now k small k happens to be the coefficient of flow which is permeability when the C page is taking place. Now identical to this would be a situation if I replace flow of fluid with flow of electricity and that is what happens you have the porous system it could be soil it could be rock it could be any other mixture any porous system. On one side there is a voltage V1 across acting electrical voltage on the other end the electrical voltage V2 and we say that V1 is not equal to V2 if V1 is equal to V2 there will not be any electrical flow taking place. So if I want to define I, I is nothing but the current. So here the equation becomes J gets a place by I, phi is nothing but the conductivity coefficient of the flow for electricity or the ions alright. So this is where we use the term sigma, now sigma is nothing but the conductivity electrical conductivity of the porous media. What about X? X is nothing but the driving force so what is causing this force to this current to pass through the media is nothing but voltage gradient so delta V upon L is nothing but differential voltage acting across the sample which is causing current to pass through this. So these are two good similes which are normally used in geotechnical engineering. I am sure that you must be aware that electrical analogy has been used to define the discharge through porous system is it not other than dam retaining balls sheet piles and so on. So this is where we use the concepts of Ohm's law. Now this is very important to understand what I have written over here that if flow does not change the fabric and stress state of the porous media that means for all practical purpose nothing happens to the porous system it remains as control volume alright. So it is something like this that the flux passes through one point without altering its stress state and the fabric structure when we say fabric structure the green size distribution comes into the picture and we are saying that that remains intact the density is also not changing. The second part of the statement is then flow rate J relates linearly to its corresponding driving force. Now this is an assumption that we are assuming a linear relationship between the flow the flux the driving force and the material property. So if you extend this analogy further let us say to the thermal energy field. So what you notice here is I am sorry this T has gone up this is basically T1 the temperature acting on the one side of the porous system at the one end and on the other end the temperature is T2 where T1 is greater than T2. Now this flow is nothing but flow of heat or the heat flux we assume here that T1 is greater than T2. So the direction of flow of heat is from left to right if L is the length of the porous system we can define gradient of heat as delta T by L where delta T happens to be the temperature difference divided by length of the sample multiplied by capital K. So capital K would be what how do you define this what is small k this is coefficient of hydraulic conductivity small k is it not sometimes you say coefficient of permeability or hydraulic conductivity what is sigma electrical conductivity what is capital K thermal conductivity clear. So this is nothing but thermal conductivity term. So if you know the thermal conductivity of the material which happens to be a very peculiar value similarly electrical conductivity of a system is going to be a peculiar value similarly a small k hydraulic conductivity of the porous system is going to be a peculiar value clear. So if you use Fourier's law what we come to is that the total flow of heat is nothing but k into thermal gradient now if I extend it further to chemicals alright. So one side of the sample there is a concentration of C1 another side of the sample there is a concentration of C2 and then because of the concentration difference if C1 is not equal to C2 and what we are assuming the way I have shown the arrow over here or the flow of concentration migration C1 is more than C2. So if I define the flux delta C as C1 minus C2 the gradient is delta C by L which is proportional to JD what is JD the chemical flux and capital D comes over here which will be the coefficient of conductivity of chemicals through the porous system how do you name this as this will be diffusion coefficient clear. So what we have done is we have diffusion coefficient now can you give me a practical example where would you find this type of situation occurring in nature. So what we have done is the classical example of chemical flow through the porous system what you are saying is also correct Sangita. If you dump industrial waste on this side of the porous system and suppose this happens to be a freshwater supply or a dead end or this could be hard rock. So this is a differential gradient between the concentration and hence now you can make out that there will be a flux of concentration migrating through the porous system. So these are the four types of flows which are normally talked about that is simple fluid, simple electricity, simple heat and simple chemical activity. Now there could be a situation where you may have to talk about the combination of these fields that means there could be hydraulic conductivity associated with contaminant transport and these contaminants might be having very high temperatures. So this becomes a multiple attribute problem you have done modeling for the fluid flow through the soil mass is it not it is very easy either by Pauling head method or by constant head method you have obtained value of k small k hydraulic conductivity or coefficient of permeability. So what you did is you measure the discharge you measure delta H by L and if these two are known you could get the value of k. Similarly I can measure the current passing through the porous system I can find out what is the voltage difference across the two end divided by the length of the sample I can get the conductivity how about this case I know what is the amount of heat migrating through the system how would you find it out when you said yes so you should answer this unfortunately it is not so easy. So any guess how would you measure q value the heat flux which is migrating through the system so 10 plus 2 physics yes please sorry calorimeter no idea is to obtain q from the porous media that control volume you cannot use calorimeter here but yes your answer is partially correct. So if I want to know value of q I have to use calorimeter definitely but now can you correct the answer which you have given try again. So from calorimeter what you will obtain specific heat of the soil so how would you compute q ms into delta theta clear. So if you know the specific heat of the soil multiplied by the mass of the sample multiplied by delta theta that comes out to be q. So that q you have to compute and put it over here to get the value of capital K. So delta theta gets cancelled out if you use the equation m into s into delta theta or delta t. So this will be equal to capital K delta theta delta t divided by l. So this will be m into s into l equal to k. So this is one of the ways of defining the k value or finding out the k value. So what I wanted to demonstrate here is once you migrate from fluid and electric field to heat and chemical field what happens a degree of complexity increases alright. In fluid flow you could measure things directly even electrical field also you could measure things directly but when it comes to heat and chemical field you cannot measure things directly what you have to do is you have to conduct some other experiments to supplement your findings and then from the combination of these two you can get the parameters alright. Now most tricky thing would be the chemical flux the most notorious and most tricky of the lot. So we will be spending enough time in talking about how chemical flux migration can be studied in the porous system and for the time being what I will do is I will skip discussion on electricity migration and heat migration through the porous media and what I intend to do is after finishing the chemical characterization I will talk about these two types of characterization is this okay. Do you find the flow okay now I am sorry I could not help it because you have to jump from one to another to another subsection only then I think you can give you complete picture of what is happening here everything is linked with each other. Now when we talk about chemical flux the law which governs the chemical flux is known as fixed law alright. Now if I ask you a question seepage flow would be governed by which equation or by which law out of the four Darcy's law consolidation mechanism Darcy's law compressibility characteristics of saturated soils Darcy's law. So where would you use Ohm's law Fourier's law and Fick's law that is right so the moment you add contaminants to the water or the fluid which is flowing through then you will notice that other three come into the picture and I am sure that you will agree that that would be the most realistic situation as the baseline we can always say that whatever migrates through porous system cannot be in the most pure form of a fluid. So that is where this type of modeling becomes very easy and challenging is this part clear any doubts? Sitchit you like to add something here yes please what is the source of heat say solar cone which you are designing. So top surface happens to be exposed to the water and water is exposed to the atmosphere or the sun directly. So what is that elevated temperature and thick layer of the soil is in contact with water on one side and on the other side it is in contact with the bedrock. So this becomes interesting situation where thermal flux is acting across the porous media. Another good example would be landfills so all landfill liners they are exposed to very high thermal gradients why whatever you are dumping in the landfills would be at elevated temperature and the other side of the liner is exposed to the soil mass or the water table and so on. So again there is a thermal gradient the same is true when we talk about chemical gradient also in case of solar ponds or in case of landfills where one surface or one side of the porous system is exposed to very high concentration other side is exposed to low concentration. As Sangeeta and Jain said there could be some other situation where you are doing too much soils and then plants may uptake that also becomes a case of chemical migration and freshwater supply in which the salt water is time to migrate. So this becomes salt water intrusion problem and so on. So this is the general law which talks about how flow can be modeled in the porous system. Now let me ask you a question we have been talking about the porous media several times what we have defined here is how flow of a flux is taking place. So my question to you is what are the attributes of the porous system and how they are going to be included in this type of formulation is the question clear? See we have talked about the energy flux which is passing through the porous system so one part of the problem is over. The second part of the problem is how would you depict or how would you characterize the porous media itself what parameters attributes are required porosity alright. So when you say porous media the name itself suggests that this system should have porosity clear. Now if I replace these materials with steel now what happens then a mechanical no flow will be flow why if I put different voltages across a steel wire or steel plate or whatever there will be flow of electricity is it not. So that goes into the realm of mechanical engineering where you are going to study the response of the metals or metallurgists they will be talking about the response of the metals and their compositions and so on. Now what we are interested in is here when we say porous media any system which contains pores in the realm of porous system what should be another attribute of the porous media so one is porosity second one. So as a black box let us say we are talking about porous system that is not going to the details of that correct so one module is porosity of the system then those parts which you are trying to figure out they fall into the micro characteristics of the porosity. Another module would be one is porosity second one how would you describe a porous system a material or a system having porosity and state of saturation is it not how much moisture is present clear so the second attribute would be the state of moisture which is either distributed or present in the media now let us see one by one how energy flux affects the state of moisture distribution in the soil sample is this part okay is the question clear to you so we are talking about two attributes one is porosity another one is state of saturation now this is how we define the porous media fluid flow till now you have been studying only migration of water suppose if I give you a saturated sample of soil with millipore water okay distilled water and through this sample let us say salt water is migrating now what is going to happen the density of salt water is more than distilled water or less what do you speculate what type of flow is going to take place what is the mechanism of the flow now something is going to change or it does not matter so what is going to change salt water comes into the pores and replaces distilled water why because of the density that is why so this becomes a density driven flow is this part clear so we have now raised the complexity of even simple seepage problem where not only Darcy law is going to valid we are going to talk about the density driven flow as well and I am sure that you will appreciate that this situation is going to be more practical where the density contrast is going to create flow of water molecules or the fluid molecules in the system let us talk about the electricity water can be polarized because of application of electrical gradient good example is electrophoresis think of a situation where the soil sample which was uniformly and fully saturated before application of any electric field because of the electrical field application it becomes polarized clear so what you have done you have altered the state of the porous system just because of electrical gradient now this problem is not same as the one where the porous media happens to be fully saturated non polarized let us come back to the fluid flow again take a completely dry sample of soil apply h1 and h2 whatever flow is going to take place did you follow the question sorry yes so suppose if I say that this state of saturation the sample is 0 there is no moisture in the sample it is a completely dry sample and then I am applying h1 on one side h2 on one side now what is going to happen to the sample why it happens exactly but why it is going to happen because of the capillary reaction so once the capillary come into the picture whatever flow is going to govern the process unsaturated soil flow clear so that means from a saturated state of the material we have now altered our discussion to unsaturated flow occurring in the porous system so lot of complexities can be created just by creating the type of the material its saturation state its porosity and so on is this part clear now I would like to ask you a question is this situation where I can even talk about the porosity change sorry in case of consolidation excellent that is right that is correct is it not so you are loading the sample what happened why it is keep on changing any other much complicated situation than this ok let us not complicated thing let us assume that this system happens to be isotropic and homogeneous we are trying to understand the mechanisms right now so let us not complicate the porous system as such though we are trying to do it as much as we can yeah so yes this is right correct very good so there could be a situation where the flow is taking place through soils which are highly active clear so what happens you started with certain volume of the soil sample and because of its swelling and shrinkage characteristics the porosity does not remain same perfectly all right now this is what is known as Mr. Ja this is what is known as everybody is talking about THM model these days it is in fashion THM model thermo hydromechanical models of soils is it not so this is where lot of research is being conducted to understand how porosity of the system changes when it comes in contact with water or when it comes in contact with some thermal flux a good example would be any barrier system or a buffer system which you are creating on one side it is exposed to thermal flux other side may be exposed to the environment when it comes in contact with water also so what happens no longer the porosity remains constant the porosity keeps on changing because of the thermal flux so I am sure that you must have realized that it is not so easy to define what type of flow is going to take place through porous system it is a very very complicated phenomena but then we have to understand the basics first so what I intend to do in my lecture today is I will try to give you the basics of the flux migration in the porous system though I have talked about a lot how complexities can be involved into this either in terms of the flux which is passing through or in terms of the material properties which may remain constant which may not remain constant any doubts or questions it is a big theme which I have talked about just now so most of the research in geotechnical engineering is right now focus in this direction particularly nuclear industry the porous system itself gets altered because of very active state of the material that is very good correct how would you define this type of phenomena what is going to happen to the soil mass or the porous system either clogging or the worst situation would be dissolution that is right or even worse than that corrosion of the porous system so you may create big big voids or the cavities in the soil mass alright or the porous system itself may get decay because of the chemical activity too much of interaction prolonged interaction or who knows your porous system might be having lot of biological entities which may get degraded in the due course of time so all those things can be put together to model ultimately how contaminants are going to migrate from one point to another point and this is where I have used the word state of contaminants in the porous system